Until now, the question of equivariance properties has not received much attention from the field.
The CNN-based jet image approach, which respects an approximate 2D translational symmetry, was for a long time the only example of an equivariant architecture that had been studied.
While translation equivariance has proved highly useful in image processing tasks, it is unclear whether it is physically meaningful in the context of jet substructure.
Very recently, it has been proposed to consider a more physically-relevant class of equivariance, specifically, the Lorentz Group Network[1]}. The LGN architecture operates at the constituent level and is fully equivariant with respect to arbitrary lorentz transformations.
However, the LGN has not yet proved to work as well as existing methods, possibly due to the exceedingly large memory structures required to implement sufficiently complex networks.
